I have a 3D surface given in data-points of the form ${x,y,z}$. What is the easiest way to get the interpolated value $z=f(X,Y)$ for given coordinates ${X,Y}$ (which are of course not in the data list)?

+1. Note that Interpolation only works on structured grids, while on unstructured ones the interpolation order will be reduced to 1, which in most cases will not be good enough. Try deleting one of the points from your regular grid to see what I mean.
–
Leonid ShifrinApr 26 '12 at 16:03

@LeonidShifrin right, and to get use an unstructured grid, one must rely on splines, likely NURBS. I have not used the mma functionality for that, though.
–
rcollyerApr 26 '12 at 16:13

@LeonidShifrin Wow, it's much worse on an unstructured grid. I wonder if there's a (good) way to fill in the missing element to create a structured grid such that the interpolation is only really bad near the refilled grid point.
–
Eli LanseyApr 26 '12 at 16:23

Mathematica is a registered trademark of Wolfram Research, Inc. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith.